What is the solution set of this system of equations?
y=x2-3x-4
x=y+8
a {(-1.0), (4.0)}
b. {(8.0). (0.8)}
c. {(0.0)}
d. {(2. -6)
e
there is no real solution.
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No real solutions.

Step-by-step explanation:

I'm going to subtract the second expression for y and plug it into the first equation.

So solving x=y+8 for y by subtracting 8 on both sides gives us y=x-8.

I'm going to insert this for the first y like so:

Now I'm going to move everything to one side.

I'm going to subtract x on both sides and add 8 on both sides.

Simplifying:

Now our job since the coefficient of x^2 is 1 is to find two numbers that multiply to be 4 and at the same time add up to be -3. I can't think of any such numbers.

Let's check the discriminant.

Compare to .

So .

The discriminant is .

So plugging in our numbers we get .

Time to simplify:

So since the discriminant is negative, then the solutions will not be real.

explanation:

infrared radiation has wavelength in the range between 700 nm and 1 mm. lets' convert these values into scientific notation, keeping in mind that:

let's start from the lower value, we have:

(we moved the dot two places to the left, so we increased the exponent by 2 units, from -9 to -7)

the higher value is:

so, the range of wavelength of infrared radiation is: